Topic 1: Multiscale Methods in Computational Fluid Dynamics. Explore stabilized and variational multiscale methods in computational fluid dynamics with a focus on advective-diffusive equations, the Boltzmann equation, and the compressible and incompressible Navier-Stokes equations. Computational Science, Engineering, and Mathematics 397 (Topic: Stabil/Multiscale Meths in CFD) and 397 (Topic 1) may not both be counted.

Topic 2: Nonlinear Static and Dynamic Finite Element Analysis. Explore code architecture and fundamental analytical technologies used in the nonlinear finite element and isogeometric analysis of solids and structures. Computational Science, Engineering, and Mathematics 397 (Topic: Nonlin Stat/Dyn Fin Elem Anly) and 397 (Topic 2) may not both be counted.

Topic 3: Validation and Uncertainty Quantification in Computational Models. Assess reliability of computational models of physical systems through validation and uncertainty quantification. Develop uncertainty analysis in terms of Bayesian probability and inference, and techniques for probabilistic model validation. Computational Science, Engineering, and Mathematics 397 (Topic: Validatn & Uq in Comptl Models) and 397 (Topic 3) may not both be counted.

Topic 4: Computational Modeling of the Cardiovascular System. Explore mathematical models and simulation of the cardiovascular system, with an emphasis on the biomechanical function of the heart, heart valves, and the vasculature. Analyze mathematical models at the level of single cells, tissues, and whole organs. Discuss image-to-model software basics to allow creation of a model of choice from any available imaging data for a project of interest. Computational Science, Engineering, and Mathematics 397 (Topic: Comptl Modlg Cardiovasc Sys) and 397 (Topic 4) may not both be counted.

Topic 5: Biomechanics of Tissues, Scaffolds, and Cells. Discuss biosolid mechanics, covering the complex mechanical behaviors of living tissues and related biomaterials, with a focus on modeling how they respond under loading. Examine major application areas to provide context to the theory and applications. Explore necessary mathematical, mechanics, and biological fundamentals in the context of applications and problems in biomedical research and medical devices. Computational Science, Engineering, and Mathematics 397 (Topic: Tissue/Scaffold Biomechanics) and 397 (Topic 5) may not both be counted.

Topic 6: Introduction to Computational Oncology. Develop a familiarity with the common computational techniques used in modeling various aspects of cancer at multiple spatial and temporal scales. Investigate how computational modeling offers unique and complementary information to traditional methods of cancer research. Examine the integration of theory and experiment while identifying the current barriers preventing computational modeling from having a broader impact on both cancer biology and clinical oncology. Computational Science, Engineering, and Mathematics 397 (Topic: Intro to Comptatnl Oncology) and 397 (Topic 6) may not both be counted.

Topic 7: Introduction to Mathematical and Physical Biology. Discuss the common mathematical and physical techniques used in modeling various aspects of biology at multiple spatial and temporal scales. With emphasis placed on the integration of theory and experiment, identify the current barriers preventing computational modeling from having a broader impact in biology. Computational Science, Engineering, and Mathematics 397 (Topic: Intro Mathematical/Phys Bio) and 397 (Topic 7) may not both be counted.

Topic 8: Biomedical Imaging: Signals and Systems. Explore the physical principles and signal processing techniques used in thermographic, ultrasonic, and radiographic imaging, including image reconstruction from projections such as CT scanning, MRI, and millimeter wave determination of temperature profiles. Computational Science, Engineering, and Mathematics 397 (Topic: Biomed Imaging: Signals/Sys) and 397 (Topic 8) may not both be counted.

Topic 9: Mathematical Physiology. Explore mathematical modeling in physiology, how physiological problems can be formulated and modeled, and how such models give rise to interesting and challenging functional features. Examine several exemplar physiological systems. Discuss the mathematical aspects of growth and remodeling in living systems, an area unique to living systems. Only one of the following may be counted: Biomedical Engineering 383J (Topic: Mathematical Physiology), 383J (Topic 14), Computational Science, Engineering, and Mathematics 397 (Topic: Mathematical Physiology), 397 (Topic 9). Same as: BME 383J.14